Wikipedia says:

*An axiom is a
sentence or proposition that is accepted as the first and last line of a one-line proof and is considered as obvious or
as an initial necessary consensus for the theory building or
acceptation. Therefore, it is taken for granted as true, and serves as a
starting point for deducing and inferencing other truths.*

This is a wrong definition. I was writing a correct definition to Wikipedia
in Finnish but theologians and philosophers were changing it. The reasons were
ideological.

The axiom is never taken for granted as true because it is a part of the
definition of the concepts.

An **axiom** is a part of the
definition of the concepts in the sentence.

We can learn the language using many methods of definition:

**Implicit**definition is a definition using axioms.

**Explicit**definition is the definition using other terms.

- An
**ostensive**definition conveys the meaning of a term by pointing out examples of what is defined by it.

- An
**operational**definition of a quantity is a specific process whereby it is measured.

- In
mathematics and computer science,
**recursion**is a particular way of specifying (or constructing) a class of objects (or an object from a certain class) with the help of a reference to other objects of the class: a recursive definition defines objects in terms of the already defined objects of the class.

- A
**stipulative**definition is a type of definition in which a new or currently-existing term is given a new meaning for the purposes of argument or discussion in a given context. This new definition may, but does not necessarily, contradict the dictionary (lexical) definition of the term. Because of this, a stipulative definition cannot be "correct" or "incorrect"; it can only differ from other definitions.

We learn words using all methods of definition.

Wikipedia says:

*In certain epistemological
theories, an axiom is a self-evident
truth upon which other knowledge must rest, and from which other knowledge is
built up. An axiom in this sense can be known before one knows any of these
other propostions. Not all epistemologists agree that any axioms, understood in
that sense, exist.*

This is wrong because

1. It is wrong to use the word “axiom” for
“self-evident truths”.

2. There are no self-evident truths.

Of course it is possible use axiomatic way to define the concepts of the
epistemology. For example Alvin I.
Goldman uses a weak definition of knowledge (in *Knowledge in a Social World*):

*“...knowledge is here
understood in the ‘weak’ sense of true belief”.*

This is partial definition of the words **knowledge**, **true** anf **belief**.

This definition assumes that you know the meanings
of the words **is**, **here**, **understand**, **weak** and **sense**.

Wikipedia says:

*In logic and mathematics,
an axiom is not
necessarily a self-evident
truth, but rather a formal logical expression used in a deduction to yield
further results. To axiomatize a system of knowledge is to show that all
of its claims can be derived from a small set of sentences that are independent
of one another. This does not imply that they could have been known
independently; and there are typically multiple ways to axiomatize a given
system of knowledge (such as arithmetic). Mathematics distinguishes two types of
axioms: logical
axioms and non-logical axioms.*

This is not exact. Axioms are implicit definitions of the fundandamental
concepts.

In Euclidean geometry following sentences will define the concepts point,
line and plane:

*“For every two points *`A`*, *`B`* there exists a line *`a`* that** contains each of the points *`A`*, *`B`*. *

*For every two points *`A`*, *`B`* there exists no more than one line that contains each of the points *`A`*, *`B`*. *

*There exists at least two points on a line. There exist at least three
points that do not lie on a line. *

*For any three points *`A`*, *`B`*, *`C`* that do not lie on the same line there exists a plane α** that contains each of the points *`A`*, *`B`*, *`C`*. For every plane there exists a point which it contains. *

*For any three points *`A`*, *`B`*, *`C`* that do not lie on one and the same line there exists no more than one
plane that contains each of the three points *`A`*, *`B`*, *`C`*. *

*If two points *`A`*, *`B`* of a line *`a`* lie in a plane α** then every point of *`a`* lies in the plane α**. *

*If two planes α**, β** have a point *`A`* in common then they have at least one more point *`B`* in common. *

*There exist at least four points which do not lie in a plane” *

The main reason to use false definitions of the
concepts is theological or philosophical. Theologians can use for example
following axioms:

*There is only one god.*

*The god is all-mighty.*

*The god is all knowing.*

*The god is all-good.*

This is one of the definitions of the Christian
god. But there is no such god. We can use axioms to define being, but it is
possible, that there is no such being.

There are mathematicians who think that the
Euclidean definition of the line is wrong. It is not wrong because it is the
definition of the Euclidean line. Non-Euclidean geometries have different
axioms.

The publishing of the dictionary is one part of
the use of the power.

Our use of the language is often weak. If
somebody asks what we mean when we say for example “science” it is probable
that we can not give a complete answer.

As atheists we can not accept the ideological
use of the weak language. Most of the theology and the philosophy is opinions using emotional and weak language.

I (Mr. Erkki Hartikainen from